JournalsrmiVol. 20, No. 1pp. 33–66

Critical nonlinear elliptic equations with singularities and cylindrical symmetry

  • Marino Badiale

    Università degli Studi di Torino, Italy
  • Enrico Serra

    Politecnico di Torino, Italy
Critical nonlinear elliptic equations with singularities and cylindrical symmetry cover
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Abstract

Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in RN\mathbb{R}^{N} with cylindrical symmetry and with singularities on a whole subspace of RN\mathbb{R}^{N}. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.

Cite this article

Marino Badiale, Enrico Serra, Critical nonlinear elliptic equations with singularities and cylindrical symmetry. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 33–66

DOI 10.4171/RMI/379